Metapopulations

Conservation Biology 55-437Lecture 14March 18, 2010

Populations are subject to demographic processes:

1)Birth

2)Immigration

3)Death

4)Emigration

Increase population size

decrease population size

Populations may be naturally patchily distributed from variation in resources, physical gradients, or biological characteristics

In some patches of a given landscape area:

•Recent colonization results in an increasing population size•In others, populations decline to local extinction•Others remain unoccupied

Natural distribution of different forest species in the Great Smoky Mountains.

Populations may be naturally patchily distributed from variation in resources, physical gradients, or biological characteristics

In some patches of a given landscape area:

•Recent colonization results in an increasing population size•In others, populations decline to local extinction•Others remain unoccupied

Patchily Distributed Populations

Disturbance and heterogeneity

Metapopulation structure

Levins (1969) introduced the concept of metapopulations to describe the dynamics of this patchiness, as a population of fragmented subpopulations occupying spatially separate habitat patches in a fragmented landscape of unsuitable habitat

• A system of populations that is linked by occasional dispersal (Levins 1969).

Levins, R. 1969. Bull. Ent. Soc. Am. 15:237-240.

Shaded areas provide an excess of individuals which emigrate to and colonize sink habitats (open).

Metapopulations

• In metapopulations, each sub-population is unstable (subject to random extinction/recolonization.

• Individual subpopulations may go extinct, though the overall population persists because some subpopulations are doing well while others are performing poorly.

• Dispersal among patches assures long term viability. Overall population

• Persistence of some local populations (sinks) depends on some migration from nearby populations (sources).

• Empty patches susceptible to colonization.

Hanski (1998) proposed 4 conditions before assuming that metapopulation dynamics explain spp. persistence

sinksource

Hanski, I. 1998. Nature 396:41−49.

i.e. persistence depends on supply from source population, some fragments may rarely receive or supply migrants

1) Patches should be discrete habitat areas of equal quality i.e. homogeneous.

2) No single population is large enough to ensure long-term survival.

3) Patches must be isolated but not to the extent of preventing re-colonization from adjacent patches.

4) Local population dynamics must be sufficiently asynchronous that simultaneous extinction of all local populations is unlikely.

Without 2 & 3: we have a ‘mainland-island’ metapopulation

Levins' Model

Based on patch occupancy modeled as the fraction of

occupied patches (f) at any given time f depends on balance

between rate of extinction e in occupied patches and

recolonization rate of empty patches c. Here, p reflects the

proportion of the population. Thus, extinctions in currently

occupied patches are represented by ep and colonization of

unoccupied patches by cp(1-p).

dp/dt = cp(1-p) - ep

Levin’s ModelEstimating persistence with metapopulation

structure:

dp/dt = cp(1-p) – ep

Here, colonization of patches cp is proportional to the number of unoccupied patches (1-p):

cp(1-p)

The growth of the population is limited by the availability of unoccupied patches (1-p).

When p is very small, almost all patches are unoccupied and available for colonization. Under these circumstances, colonization rate is ~ cp.

If e > c then the population will go extinct. Therefore, the relationship between e and c defines the extinction threshold.

When extinctions and colonizations are equally frequent: dp/dt = 0. Therefore, we can solve for p at equilibrium by setting dp/dt = 0:

p* = 1 – e/c

At equilibrium the metapopulation will persist (i.e., p* > 0) only if e < m

Levin’s ModelEstimating persistence with metapopulation

structure:

Other models:

Levins' Model makes simplistic assumptions which may not be realistic:

1. Does not account for changes in size of habitat patches

2. Degree of isolation assumed constant: distance between patches

3. Immigration rates assumed constant: e.g. migration is often among close patches

Spatially explicit: assume that local populations interact only with nearby local populations, thus migration is distance dependent

Spatially realistic models: account for variation in size of patches, total patch number and their spatial arrangement. Models are often complex and rely on detailed data

Spatially Realistic Metapopulation Models

• links metapopulation ecology with landscape ecology

M = metapopulation capacity of the fragmented landscape

or, the number of occupied patches each occupied patch will give rise to during its lifetime.

Here, the size of the metapopulation at equilibrium (p*) can be defined as:

P* = 1 – e/(cM)

Similar to Levins’ model but now the metapopulation size at equilibrium depends on both the metapopulation capacity

and a weighted average of the probabilities that the different patches are occupied.

Spatially Realistic Metapopulation Models

To identify the conditions for metapopulation

persistence:M > e/c

Need to know:

1)the scale of connectivity set by the dispersal range of the species.

2) the spatial distribution of habitat patches.

Natural example of metapopulations:

Hanski & colleagues surveyed for >10 years populations of endangered Glanville fritillary butterfly (pg. 430-431) in dry meadow patches in the Aland islands:

>4000 suitable patches: In 2005 >700 occupied

pg 431, Hanski's study of butterflies

habitat fragmentation over 20 years (1973-1993)

Predicted occupancy of patches over time, with fragmentation and habitat loss

Predicted occupancy with a further 50% loss of habitat

PVA: Quantitative Risk Analysis (PVA): Uses demographic data to understand the relationship between future survival in small or endangered populations and threats or management options. It can also predict the effect of chance events on persistence.

4 major chance association events will affect survival in small populations:

1) natural catastrophes: fire, floods, earthquakes2) genetic factors: drift, founder events, inbreeding3) environmental uncertainty4) demographic stochasticity

PVA models tend to be species specific due to differences in population size/ demography and differential responses to each of these 4 factors.

Application of PVA

1. Extinction risk is the main application: Predict probability of population decline in a given time period

2. How much land, and in what configuration, is needed to protect against extinction risk?

3. What life stages or demographic processes are in need of management?

4. How many individuals are required to establish a viable population in reintroduction programmes?

5. How many individuals can be harvested without impacting persistence?

6. Guiding future research priorities

If model outcomes are highly sensitive to certain parameters (e.g. say risk of decline is sensitive to low or high input values of juvenile survival rates) we may need more accurate field data

Two main modeling approaches: (pg. 433-434)1. Simple count-based

Counts of individuals in a population or surrogates for population size (e.g. females with offspring; males with territories)

Assumptions: all individuals are identical but fails to consider effects on population growth of age structure, size, social standing, and sex ratio (e.g. analogous to factors affecting Ne)

2. Complex Demography based

Uses data on population structure (fecundity, age-class contribution to survival, dispersal distances)

Model can be run several times using high and low values of a parameter to account for uncertainty. Problem is that it islabour intensive and costly

MVP = population size below which the probability of extinction is increased, or the minimum number of interacting local populations necessary for long-term persistence of a metapopulation

Minimum Viable Population: an important aspect of PVA models

1) Demographic uncertainty: Random events acting on survival/ reproduction that is affected by population size and structure

1) Skewed sex ratio (Dusky sea-side sparrow went extinct 1990 after flooding and habitat loss resulted in only 8 males remaining!)

2) Age structure: populations with high numbers of old or juvenile individuals (e.g. many freshwater ‘pearl’ mussel populations are dominated by old individuals which have zero recruitment potential)

2) Environmental uncertainty: resource fluctuations, seasonal variation, densities of enemies

4 factors are very important in PVA models:

3. Natural catastrophes e.g. floods will affect persistence time regardless of population size- some endangered species are broken up into separate populations to avoid this problem

4. Inbreeding: only relevant to very small populations

Endemic to southeastern USA in mature deciduous forests: Pine-wiregrass savannah

•Nests only in living pine trees >80 yrs: can accommodate nest cavities

• Threats: Habitat loss has a severe effect on populations

Endangered: Small, fragmented & isolated populations

PVA Examples: Red cockaded woodpecker

1) Is the current distribution consistent with long term regional persistence?

2) What changes in management would promote this?

Maguire et al. (1995) PVA in Georgia Piedmont

• Input data from active colonies: newly banded inds. 1983-1988

Five age-classes & different life-history stages

Used 2 datasets: One based on banded individuals only

One based on banded & unbanded individuals

• Estimated age-dependent survival and fecundity of females

• Incorporated demographic and environmental uncertainty

1. Data from banded inds: Median time to extinction was 58 years but was highly variable and affected by demographic stochasticity which could ↓ time to extinction to 40 years;

2. Including data from un-banded birds: zero extinction probability in 100 yrs and in population size

Also ran sensitivity analysis: Important in choosing between management options

For Banded data: λ (finite rate of increase) and extinction risk were most sensitive to variation in juvenile survival. When they reduced juvenile survival by 10%, and λ = 0.913 and there was a faster time to extinction

When Non-banded data was included: same decrease gave λ = 1.03 which corresponded with a growing population and zero extinction risk.

Why such uncertainty? Un-banded survey likely counted some birds more than once, thus they overestimated the population

Prudent conservation: Reduce fledgling mortality by providing more suitable nesting cavities (which are limiting)

Florida (West Indian) manatee: Endangered species with around 2000 individuals. Up to 5.3% of population dies per year, often due to boating accidents. 50% (220) of female carcasses reproductively mature

PVA of Marmontel et al. (1997) on Florida manatees:

Determined age-specific data on survival and reproduction using 1200 carcasses obtained between 1977 and 1992

For the current λ value

PVA predicted only a 44% chance of persisting for 1000 years

Outlook poor:

Are there management actions that could increase persistence?

Current λ estimated at: 0.997 (remember: if λ < 1 the population will decline)

Re-ran the model using a sensitivity analysis asking what effect a 10% reduction in adult mortality would have on extinction risk

Would result in λ >1 and enhance long term viability

Management options?Use speed control zones to reduce mortality from propeller injuries

Series of protected areas linking boreal populations of several carnivore species with small, more-isolated populations in southern range margins.

Conservation efforts have focused on retaining landscape connectivity in this region.

Carroll, et al. 2003. Ecological Applications 13:1773−1789.

Large Carnivores in the Rocky Mountains

Spatially Explicit Population Models (SEPMs)

• combine demographic data with habitat characteristics to predict whether patches of suitable habitat will remain occupied over time.

SEPM modeling is beneficial as can add information on:

1)response of a population to landscape change, including highlighting areas of highest vulnerability to decline or extinction.

2)location of population source areas

3)response of the populations to alternative conservation strategies.

• Different habitats may be associated with different demographic rates.

• Demographic rates can be scaled to reflect the different habitat patches in the landscape.

Spatially Explicit Population Models (SEPMs)

Poorer habitat higher mortality and lower reproductive output.

Spatially Explicit Population Models (SEPMs)

• However, the human population can change over time.

• Model can be changed to accommodate different landscape change scenarios through changing human-associated impact factors (roads and human populations).

• Can also be modified to incorporate time lags in landscape change (e.g., humans change landscape faster than animals can respond).

Spatially Explicit Population Models (SEPMs)

• With current conservation efforts, each species will face reductions in landscape occupancy over next 15 years.

• So, additional conservation efforts are needed.

Spatially Explicit Population Models (SEPMs)

• Economically, you cannot preserve all of the habitat so you need to find the ‘biggest bang for the buck’.

Spatially Explicit Population Models (SEPMs)

Whole region

Canadian Rockies ecoregion

ReferencesAbrams, P.A. 2002. Will small population sizes warn us of impending extinctions? American

Naturalist 160:293-305.Carroll, C., R.F. Noss, P.C. Paquet and N.H. Schumaker. 2003. Use of population viability

analysis and reserve selection algorithms in regional conservation plans. Ecological Applications 13:1773−1789.

Doak, D.F. 1995. Source-Sink models and the problem of habitat degradation: general models and applications to the Yellowstone Grizzly. Conservation Biology 9:1370-1379.

Donovan, T., R. Lamberson, A. Kimber, F. Thompson III and J. Faaborg. 1995. Modeling the effects of habitat fragmentation on source and sink demography of neotropical migrant birds. Conservation Biology 9: 1396-1407.

Dunning, J.B. et al. 1995. Spatially explicit population models: current forms and future tests. Ecological Applications 5:3-11.

Gilpin, M. 1991. The genetic effective size of a metapopulation. Biological Journal of the Linnean Society 42:165-175.

Hanski, I. 1991. Metapopulation dynamics: brief history and conceptual domain. Biological Journal of the Linnean Society 42:3-16.

Hanski, I., T. Pakkala, M. Kuussaari and G. Lei. 1995. Metapopulation persistence of an endangered butterfly in a fragmented landscape. Oikos 72:21-28.

Levins, R. 1969. Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the Entomological Society of America 15:237-240.

Maguire, L.A., G. Wilhere and Q. Dong. 1995. Population viability analysis for red-cockaded woodpeckers in the Georgia piedmont. Journal of Wildlife Management 59:533-542.

Meffe, G. and C.R. Carroll. 1997. Principles of Conservation Biology. SinauerMarmontel, M., S.R. Humphrey and T. O'Shea. 1997. Population viability analysis of the Florida

manatee (Trichechus manatus latirostris), 1976-1991. Conservation Biology 11:467-481.Opdam, P., R. Poppen, R. Reijnen and A. Schotman. 1994. The landscape ecological approach

in bird conservation: integrating the metapopulation concept into spatial planning. IBIS 137:139-146.

Wielgus, R.B. 2002. Minimum viable population and reserve sizes for naturally regulated grizzly bears in British Columbia. Biological Conservation 106:381-388.